Query Conservative Extensions in Horn Description Logics with Inverse Roles

We investigate the decidability and computational complexity of query conservative extensions in Horn description logics (DLs) with inverse roles. This is more challenging than without inverse roles because characterizations in terms of unbounded homomorphisms between universal models fail, blocking the standard approach to establishing decidability. We resort to a combination of automata and mosaic techniques, proving that the problem is 2EXPTIME-complete in Horn-ALCHIF (and also in Horn-ALC and in ELI). We obtain the same upper bound for deductive conservative extensions, for which we also prove a CONEXPTIME lower bound.